N5 Prelim Revision Booklet - Web Version

N5 Formula Sheet

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Volume

Hint

The formula sheet shows how to calculate the volume of a sphere.

Answer

\(7400\text{ cm}^3\)

Solution

Hint

What is the height of the cylinder itself, without the hemisphere on top?

Answer

\(3900\text{ cm}^3\)

Solution

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Substitute the values you know into the formula provided on the formula sheet.

Answer

\(10.0\text{ cm}\)

Solution

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Equations and Inequations

Hint

Be very careful if you find yourself dividing by a negative number. It is usually best to avoid it.

Answer

\(3>x\) or \(x<3\)

Solution

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The bracket in the first line is being multiplied by negative 2.

Answer

\(x<\frac{3}{2}\) or \(\frac{3}{2}>x\)

Solution

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Multiplying through carefully by the denominator will deal with the fraction.

Answer

\(x=\frac{13}{2}\)

Solution

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Multiplying by the denominator is a good strategy even when the denominator contains a letter.

Answer

\(x=3\)

Solution

Hint

Find an expression for the perimeter of each shape first. You are told they have equal perimeter...

Answer

\(10\text{ cm}\)

Solution

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Circle Geometry

Hint

Look for right-angles, and isosceles triangles.

Answer

\(\angle ABD=61^{\circ}\)

Solution

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Look for right-angles, and isosceles triangles.

Answer

\(\angle PQR = 34^{\circ}\)

Solution

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Scientific Notation

Hint

Make sure you can enter numbers in scientific notation into your calculator to perform calculations.

Answer

\(8.72\times10^{10}\text{ miles}\)

Solution

Hint

Make sure you can enter numbers in scientific notation into your calculator, and consider whether they should be put them in brackets when performing calculators.

Answer

\(18\)

Solution

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Expanding Brackets

Hint

Take care with negatives when expanding brackets.

Answer

\(6x^2+5x-3\)

Solution

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Check the six terms obtained from expanding these brackets are correct carefully before you collect like terms.

Answer

\(x^3+2x^2-13x+10\)

Solution

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Take care with multiplying a negative by a negative.

Answer

\(2x^3-5x^2-13x-4\)

Solution

Hint

Tackle the expansion of \((x-3)(x+1)\) then consider the "\(-\)" that lies in front of it.

Answer

\(-x+3\)

Solution

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Similar Shapes

Hint

Draw the two triangles separately.

Answer

\(x=6\)

Solution

Hint

Obtain the LSF first, and then think about which scale factor is needed.

Answer

\(7500\text{ cm}^3\)

Solution

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Percentages

Hint

"100% + 2.5%"

Answer

\(£344.61\)

Solution

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What does appreciate mean?

Answer

\(£148 000\)

Solution

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What percentage of their original pay is £11.18?

Answer

\(£10.75\)

Solution

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Without a calculator, finding 1% will be awkward. What other percentage could be reached, which would let you then find 100% quickly?

Answer

\(32\)

Solution

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Numerical Fractions

Hint

When multiplying (or dividing) factions, the denominators don't need to be the same. However, you don't want either to be a mixed fraction.

Answer

\(\dfrac{26}{11}\) or \(2\dfrac{4}{11}\)

Solution

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How can a division by a fraction be rewritten as a multiplication?

Answer

\(\dfrac{20}{9}\) or \(2\dfrac{2}{9}\)

Solution

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When adding (or subtracting) fractions, the denominators need to be equal.

Answer

\(\dfrac{193}{30}\) or \(6\dfrac{13}{30}\)

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Pythagoras

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Straight Lines

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Functions

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Factorising

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Statistics

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Quadratics

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Arcs and Sectors

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Changing the Subject

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Surds

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Indices

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Trig Graphs

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Simultaneous Equations

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Area and Sine Rules

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Algebraic Fractions

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Solution

NOTE: To use the widgets in the compiled HTML file, you need to have a JavaScript-enabled browser.

Fill-In-The-Blanks (fitb())

Create fill-in-the-blank questions using fitb(), providing the answer as the first argument.

• 2 + 2 is

You can also create these questions dynamically, using variables from your R session.

• The square root of 49 is:

The blanks are case-sensitive; if you don't care about case, use the argument ignore_case = TRUE.

• What is the letter after D?

If you want to ignore differences in whitespace use, use the argument ignore_ws = TRUE (which is the default) and include spaces in your answer anywhere they could be acceptable.

• How do you load the tidyverse package?

You can set more than one possible correct answer by setting the answers as a vector.

• Type a vowel:

You can use regular expressions to test answers against more complex rules.

• Type any 3 letters:

Multiple Choice (mcq())

• "Never gonna give you up, never gonna: let you goturn you downrun awaylet you down"
• "I bless the rainsguess it rainssense the rain down in Africa" -Toto

True or False (torf())

• True or False? You can permute values in a vector using sample(). TRUEFALSE

Longer MCQs (longmcq())

When your answers are very long, sometimes a drop-down select box gets formatted oddly. You can use longmcq() to deal with this. Since the answers are long, It's probably best to set up the options inside an R chunk with echo=FALSE.

What is a p-value?

the probability that the null hypothesis is true the probability of the observed, or more extreme, data, under the assumption that the null-hypothesis is true the probability of making an error in your conclusion

What is true about a 95% confidence interval of the mean?

if you repeated the process many times, 95% of intervals calculated in this way contain the true mean 95% of the data fall within this range there is a 95% probability that the true mean lies within this range

Checked sections

Create sections with the class webex-check to add a button that hides feedback until it is pressed. Add the class webex-box to draw a box around the section (or use your own styles).

I am going to learn a lot: TRUEFALSE

What is a p-value?

the probability that the null hypothesis is true the probability of the observed, or more extreme, data, under the assumption that the null-hypothesis is true the probability of making an error in your conclusion

Hidden solutions and hints

You can fence off a solution area that will be hidden behind a button using hide() before the solution and unhide() after, each as inline R code. Pass the text you want to appear on the button to the hide() function.

If the solution is an RMarkdown code chunk, instead of using hide() and unhide(), simply set the webex.hide chunk option to TRUE, or set it to the string you wish to display on the button.

Recreate the scatterplot below, using the built-in cars dataset.

I need a hint

See the documentation for plot() (?plot)

Click here to see the solution

plot(cars$speed, cars$dist)